Font Size: a A A

Certain Nonlinear Operators And Nonlinear Equations Discussed

Posted on:2004-11-09Degree:DoctorType:Dissertation
Country:ChinaCandidate:W X WangFull Text:PDF
GTID:1110360095950023Subject:Basic mathematics
Abstract/Summary:PDF Full Text Request
The purpose of this paper is to discuss two classes of nonlinear equations, one of which is nonlinear operator equations with concavity or convexity and the other is nonlinear integro-difFerential equations in Banach space.By means of partial ordering method and iterative techniques, the existence of solutions for these nonlinear equations is studied.This paper includes three chapter.Chapter 1. Introduction. In the first chapter we provide a research summary of the operators with concavity or convexity since the beginning when these definitions of concave (convex) operator were introduced . and the general thoughts in which we can deal with the nonlinear integro-differential equations in Banach space.Chapter 2 Fixed Point Theorems of Concave(Convex) Operators and Applications. The chapter is devoted to the existence and uniqueness of fixed point of monotone operators with concavity or convexity. In 2.1. we present some relations: among the various concave operators, among the various -convex operators. In particular, we give a series of sufficient and necessary conditions for the existence and uniqueness of fixed point of increasing operators with u0-concavity and decreasing operators with -u0-convexity. Moreover, we discuss increasing operators with order concavity, decreasing operators with order convexity and mixed monotone operators with u0-concavity and convexity.In 2.2, we give a series of sufficient conditions for the existence and uniqueness of fixed point of increasing operator with u0-convexity or Q(> 1)- homogeneity.In 2.3, we apply the abstract results in 2.1 and 2.2 to nonlinear Hammerstein integral equations.Chapter 3 Integro-differential Equations in Banach Space . In this final chapter, our purpose is to investigate the existence of maximal and minimal solutions of second-order integro-difTerential equations in Banach Space by results of first-order integro-differential equations in Banach Space. In 3.1, by establishing comparison results, we study the existence of maximal and minimal solutions of initial value problems and boundary value problem for first-order integro-differential equations with nonlinear operator in Banach Space as follow:where,In 3.2. we discuss the initial value value problems and boundary value problem for second-order integro-differential equation of mixed type in Banach space as follow:And give some results of maximal and minimal solutions of them.In 3.3 and 3.4, following the same idea as 3.3 and 3.4, we discuss the existence of maximal and minimal solutions of first-order and second-order impulsive integro-differential equations corresponding to the equations in 3.1 and3.2.
Keywords/Search Tags:Nonlinear
PDF Full Text Request
Related items